#include <AppDef_TheLeastSquares.hxx>

Public Member Functions
	AppDef_TheLeastSquares (const AppDef_MultiLine &SSP, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const math_Vector &Parameters, const Standard_Integer NbPol)
	given a MultiLine, this algorithm computes the least square resolution using the Householder-QR method. If the first and/or the last point is a constraint point, the value of the tangency or curvature is computed in the resolution. NbPol is the number of control points wanted for the approximating curves. The system to solve is the following: A X = B. Where A is the Bernstein matrix computed with the parameters, B the points coordinates and X the poles solutions. The matrix A is the same for each coordinate x, y and z and is also the same for each MultiLine point because they are approximated in parallel(so with the same parameter, only the vector B changes).

	AppDef_TheLeastSquares (const AppDef_MultiLine &SSP, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const Standard_Integer NbPol)
	Initializes the fields of the object.

	AppDef_TheLeastSquares (const AppDef_MultiLine &SSP, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const math_Vector &Parameters, const Standard_Integer NbPol)
	given a MultiLine, this algorithm computes the least square resolution using the Householder-QR method. If the first and/or the last point is a constraint point, the value of the tangency or curvature is computed in the resolution. Deg is the degree wanted for the approximating curves. The system to solve is the following: A X = B. Where A is the BSpline functions matrix computed with <parameters>, B the points coordinates and X the poles solutions. The matrix A is the same for each coordinate x, y and z and is also the same for each MultiLine point because they are approximated in parallel(so with the same parameter, only the vector B changes).

	AppDef_TheLeastSquares (const AppDef_MultiLine &SSP, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Integer FirstPoint, const Standard_Integer LastPoint, const AppParCurves_Constraint FirstCons, const AppParCurves_Constraint LastCons, const Standard_Integer NbPol)
	Initializes the fields of the object.

void	Perform (const math_Vector &Parameters)
	Is used after having initialized the fields. The case "CurvaturePoint" is not treated in this method.

void	Perform (const math_Vector &Parameters, const Standard_Real l1, const Standard_Real l2)
	Is used after having initialized the fields.

void	Perform (const math_Vector &Parameters, const math_Vector &V1t, const math_Vector &V2t, const Standard_Real l1, const Standard_Real l2)
	Is used after having initialized the fields. <V1t> is the tangent vector at the first point. <V2t> is the tangent vector at the last point.

void	Perform (const math_Vector &Parameters, const math_Vector &V1t, const math_Vector &V2t, const math_Vector &V1c, const math_Vector &V2c, const Standard_Real l1, const Standard_Real l2)
	Is used after having initialized the fields. <V1t> is the tangent vector at the first point. <V2t> is the tangent vector at the last point. <V1c> is the tangent vector at the first point. <V2c> is the tangent vector at the last point.

Standard_Boolean	IsDone () const
	returns True if all has been correctly done.

AppParCurves_MultiCurve	BezierValue ()
	returns the result of the approximation, i.e. all the Curves. An exception is raised if NotDone.

const AppParCurves_MultiBSpCurve &	BSplineValue ()
	returns the result of the approximation, i.e. all the Curves. An exception is raised if NotDone.

const math_Matrix &	FunctionMatrix () const
	returns the function matrix used to approximate the set.

const math_Matrix &	DerivativeFunctionMatrix () const
	returns the derivative function matrix used to approximate the set.

void	ErrorGradient (math_Vector &Grad, Standard_Real &F, Standard_Real &MaxE3d, Standard_Real &MaxE2d)
	returns the maximum errors between the MultiLine and the approximation curves. F is the sum of the square distances. Grad is the derivative vector of the function F.

const math_Matrix &	Distance ()
	returns the distances between the points of the multiline and the approximation curves.

void	Error (Standard_Real &F, Standard_Real &MaxE3d, Standard_Real &MaxE2d)
	returns the maximum errors between the MultiLine and the approximation curves. F is the sum of the square distances.

Standard_Real	FirstLambda () const
	returns the value (P2 - P1)/ V1 if the first point was a tangency point.

Standard_Real	LastLambda () const
	returns the value (PN - PN-1)/ VN if the last point was a tangency point.

const math_Matrix &	Points () const
	returns the matrix of points value.

const math_Matrix &	Poles () const
	returns the matrix of resulting control points value.

const math_IntegerVector &	KIndex () const
	Returns the indexes of the first non null values of A and DA. The values are non null from Index(ieme point) +1 to Index(ieme point) + degree +1.

Protected Member Functions
void	Init (const AppDef_MultiLine &SSP, const Standard_Integer FirstPoint, const Standard_Integer LastPoint)
	is used by the constructors above.

Standard_Integer	NbBColumns (const AppDef_MultiLine &SSP) const
	returns the number of second member columns. Is used internally to initialize the fields.

Standard_Integer	TheFirstPoint (const AppParCurves_Constraint FirstCons, const Standard_Integer FirstPoint) const
	returns the first point being fitted.

Standard_Integer	TheLastPoint (const AppParCurves_Constraint LastCons, const Standard_Integer LastPoint) const
	returns the last point being fitted.

void	Affect (const AppDef_MultiLine &SSP, const Standard_Integer Index, AppParCurves_Constraint &Cons, math_Vector &Vt, math_Vector &Vc)
	Affects the fields in the case of a constraint point.

void	ComputeFunction (const math_Vector &Parameters)

void	SearchIndex (math_IntegerVector &Index)

void	MakeTAA (math_Vector &TheA, math_Vector &TheB)
	computes internal matrixes for the resolution

void	MakeTAA (math_Vector &TheA)
	computes internal matrixes for the resolution

void	MakeTAA (math_Vector &TheA, math_Matrix &TheB)
	computes internal matrixes for the resolution

Constructor & Destructor Documentation

◆ AppDef_TheLeastSquares() [1/4]

AppDef_TheLeastSquares::AppDef_TheLeastSquares	(	const AppDef_MultiLine &	SSP,
		const Standard_Integer	FirstPoint,
		const Standard_Integer	LastPoint,
		const AppParCurves_Constraint	FirstCons,
		const AppParCurves_Constraint	LastCons,
		const math_Vector &	Parameters,
		const Standard_Integer	NbPol )

given a MultiLine, this algorithm computes the least square resolution using the Householder-QR method. If the first and/or the last point is a constraint point, the value of the tangency or curvature is computed in the resolution. NbPol is the number of control points wanted for the approximating curves. The system to solve is the following: A X = B. Where A is the Bernstein matrix computed with the parameters, B the points coordinates and X the poles solutions. The matrix A is the same for each coordinate x, y and z and is also the same for each MultiLine point because they are approximated in parallel(so with the same parameter, only the vector B changes).

◆ AppDef_TheLeastSquares() [2/4]

AppDef_TheLeastSquares::AppDef_TheLeastSquares	(	const AppDef_MultiLine &	SSP,
		const Standard_Integer	FirstPoint,
		const Standard_Integer	LastPoint,
		const AppParCurves_Constraint	FirstCons,
		const AppParCurves_Constraint	LastCons,
		const Standard_Integer	NbPol )

Initializes the fields of the object.

◆ AppDef_TheLeastSquares() [3/4]

AppDef_TheLeastSquares::AppDef_TheLeastSquares	(	const AppDef_MultiLine &	SSP,
		const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Mults,
		const Standard_Integer	FirstPoint,
		const Standard_Integer	LastPoint,
		const AppParCurves_Constraint	FirstCons,
		const AppParCurves_Constraint	LastCons,
		const math_Vector &	Parameters,
		const Standard_Integer	NbPol )

given a MultiLine, this algorithm computes the least square resolution using the Householder-QR method. If the first and/or the last point is a constraint point, the value of the tangency or curvature is computed in the resolution. Deg is the degree wanted for the approximating curves. The system to solve is the following: A X = B. Where A is the BSpline functions matrix computed with <parameters>, B the points coordinates and X the poles solutions. The matrix A is the same for each coordinate x, y and z and is also the same for each MultiLine point because they are approximated in parallel(so with the same parameter, only the vector B changes).

◆ AppDef_TheLeastSquares() [4/4]

AppDef_TheLeastSquares::AppDef_TheLeastSquares	(	const AppDef_MultiLine &	SSP,
		const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Mults,
		const Standard_Integer	FirstPoint,
		const Standard_Integer	LastPoint,
		const AppParCurves_Constraint	FirstCons,
		const AppParCurves_Constraint	LastCons,
		const Standard_Integer	NbPol )

Initializes the fields of the object.

Member Function Documentation

◆ Affect()

void AppDef_TheLeastSquares::Affect	(	const AppDef_MultiLine &	SSP,
		const Standard_Integer	Index,
		AppParCurves_Constraint &	Cons,
		math_Vector &	Vt,
		math_Vector &	Vc )

protected

Affects the fields in the case of a constraint point.

◆ BezierValue()

AppParCurves_MultiCurve AppDef_TheLeastSquares::BezierValue ( )

returns the result of the approximation, i.e. all the Curves. An exception is raised if NotDone.

◆ BSplineValue()

const AppParCurves_MultiBSpCurve & AppDef_TheLeastSquares::BSplineValue ( )

returns the result of the approximation, i.e. all the Curves. An exception is raised if NotDone.

◆ ComputeFunction()

void AppDef_TheLeastSquares::ComputeFunction ( const math_Vector & Parameters )

protected

◆ DerivativeFunctionMatrix()

const math_Matrix & AppDef_TheLeastSquares::DerivativeFunctionMatrix ( ) const

returns the derivative function matrix used to approximate the set.

◆ Distance()

const math_Matrix & AppDef_TheLeastSquares::Distance ( )

returns the distances between the points of the multiline and the approximation curves.

◆ Error()

void AppDef_TheLeastSquares::Error	(	Standard_Real &	F,
		Standard_Real &	MaxE3d,
		Standard_Real &	MaxE2d )

returns the maximum errors between the MultiLine and the approximation curves. F is the sum of the square distances.

◆ ErrorGradient()

void AppDef_TheLeastSquares::ErrorGradient	(	math_Vector &	Grad,
		Standard_Real &	F,
		Standard_Real &	MaxE3d,
		Standard_Real &	MaxE2d )

returns the maximum errors between the MultiLine and the approximation curves. F is the sum of the square distances. Grad is the derivative vector of the function F.

◆ FirstLambda()

Standard_Real AppDef_TheLeastSquares::FirstLambda ( ) const

returns the value (P2 - P1)/ V1 if the first point was a tangency point.

◆ FunctionMatrix()

const math_Matrix & AppDef_TheLeastSquares::FunctionMatrix ( ) const

returns the function matrix used to approximate the set.

◆ Init()

void AppDef_TheLeastSquares::Init	(	const AppDef_MultiLine &	SSP,
		const Standard_Integer	FirstPoint,
		const Standard_Integer	LastPoint )

protected

is used by the constructors above.

◆ IsDone()

Standard_Boolean AppDef_TheLeastSquares::IsDone ( ) const

returns True if all has been correctly done.

◆ KIndex()

const math_IntegerVector & AppDef_TheLeastSquares::KIndex ( ) const

Returns the indexes of the first non null values of A and DA. The values are non null from Index(ieme point) +1 to Index(ieme point) + degree +1.

◆ LastLambda()

Standard_Real AppDef_TheLeastSquares::LastLambda ( ) const

returns the value (PN - PN-1)/ VN if the last point was a tangency point.

◆ MakeTAA() [1/3]

void AppDef_TheLeastSquares::MakeTAA ( math_Vector & TheA )

protected

computes internal matrixes for the resolution

◆ MakeTAA() [2/3]

void AppDef_TheLeastSquares::MakeTAA	(	math_Vector &	TheA,
		math_Matrix &	TheB )

protected

computes internal matrixes for the resolution

◆ MakeTAA() [3/3]

void AppDef_TheLeastSquares::MakeTAA	(	math_Vector &	TheA,
		math_Vector &	TheB )

protected

computes internal matrixes for the resolution

◆ NbBColumns()

Standard_Integer AppDef_TheLeastSquares::NbBColumns ( const AppDef_MultiLine & SSP ) const

protected

returns the number of second member columns. Is used internally to initialize the fields.

◆ Perform() [1/4]

void AppDef_TheLeastSquares::Perform ( const math_Vector & Parameters )

Is used after having initialized the fields. The case "CurvaturePoint" is not treated in this method.

◆ Perform() [2/4]

void AppDef_TheLeastSquares::Perform	(	const math_Vector &	Parameters,
		const math_Vector &	V1t,
		const math_Vector &	V2t,
		const math_Vector &	V1c,
		const math_Vector &	V2c,
		const Standard_Real	l1,
		const Standard_Real	l2 )

Is used after having initialized the fields. <V1t> is the tangent vector at the first point. <V2t> is the tangent vector at the last point. <V1c> is the tangent vector at the first point. <V2c> is the tangent vector at the last point.

◆ Perform() [3/4]

void AppDef_TheLeastSquares::Perform	(	const math_Vector &	Parameters,
		const math_Vector &	V1t,
		const math_Vector &	V2t,
		const Standard_Real	l1,
		const Standard_Real	l2 )

Is used after having initialized the fields. <V1t> is the tangent vector at the first point. <V2t> is the tangent vector at the last point.

◆ Perform() [4/4]

void AppDef_TheLeastSquares::Perform	(	const math_Vector &	Parameters,
		const Standard_Real	l1,
		const Standard_Real	l2 )

Is used after having initialized the fields.

◆ Points()

const math_Matrix & AppDef_TheLeastSquares::Points ( ) const

returns the matrix of points value.

◆ Poles()

const math_Matrix & AppDef_TheLeastSquares::Poles ( ) const

returns the matrix of resulting control points value.

◆ SearchIndex()

void AppDef_TheLeastSquares::SearchIndex ( math_IntegerVector & Index )

protected

◆ TheFirstPoint()

Standard_Integer AppDef_TheLeastSquares::TheFirstPoint	(	const AppParCurves_Constraint	FirstCons,
		const Standard_Integer	FirstPoint ) const

protected

returns the first point being fitted.

◆ TheLastPoint()

Standard_Integer AppDef_TheLeastSquares::TheLastPoint	(	const AppParCurves_Constraint	LastCons,
		const Standard_Integer	LastPoint ) const

protected

returns the last point being fitted.

The documentation for this class was generated from the following file:

AppDef_TheLeastSquares.hxx

Public Member Functions

Protected Member Functions

Constructor & Destructor Documentation

◆ AppDef_TheLeastSquares() [1/4]

◆ AppDef_TheLeastSquares() [2/4]

◆ AppDef_TheLeastSquares() [3/4]

◆ AppDef_TheLeastSquares() [4/4]

Member Function Documentation

◆ Affect()

◆ BezierValue()

◆ BSplineValue()

◆ ComputeFunction()

◆ DerivativeFunctionMatrix()

◆ Distance()

◆ Error()

◆ ErrorGradient()

◆ FirstLambda()

◆ FunctionMatrix()

◆ Init()

◆ IsDone()

◆ KIndex()

◆ LastLambda()

◆ MakeTAA() [1/3]

◆ MakeTAA() [2/3]

◆ MakeTAA() [3/3]

◆ NbBColumns()

◆ Perform() [1/4]

◆ Perform() [2/4]

◆ Perform() [3/4]

◆ Perform() [4/4]

◆ Points()

◆ Poles()

◆ SearchIndex()

◆ TheFirstPoint()

◆ TheLastPoint()